Question

Determine the quotient, q(x), and remainder, r(x) when

f(x) = 12x4 + 22x3 + 30x2 + 28x + 8

is divided by g(x) = 4x2 + 2x + 6 .

Answer 1

Quotient:

`q(x) = 3 {x}^(2) + 4x + 1`

Remainder:

`r(x) = 4x + 2`

Step-by-step explanation

The given function is:

`f(x) = 12 {x}^(4) + 2 {x}^(3) + 30 {x}^(2) + 28x + 8`

and

`g(x) =4 {x}^(2) + 2x + 6`

We want to determine the quotient and the remainder when f(x) is divided by g(x).

We perform the long division as shown in the attachment.

The quotient is

`q(x) = 3 {x}^(2) + 4x + 1`

and the remainder is

`r(x) = 4x + 2`